Users of high carbon steel sheets as tools, automotive parts (gear and transmission), and the like request excellent workability because these steel sheets are formed in various complex shapes. In recent years, on the other hand, requirement of reduction in the cost for manufacturing parts increases. Responding to the requirement, some working processes are eliminated and working methods are changed. For example, as the forming technology of automobile driving system parts using high carbon steel sheets, there was developed a double-acting forming technique which allows applying thickness-additive forming process and realizes significant shortening of manufacturing process, and the technique has been brought into practical applications in a part of industries, (for example, refer to Journal of the JSTP, 44, pp. 409-413, (2003)).
Along with that movement, the high carbon steel sheets face ever-increasing request of workability to attain higher ductility than ever. Since some of the parts are often subjected to hole-expansion (burring) treatment after punching, they are wanted to have excellent stretch-flange formability.
Furthermore, from the viewpoint of cost reduction accompanied with increase in the product yield, these steel sheets are strongly requested to have homogeneous mechanical properties. In particular, the homogeneity of hardness in the sheet thickness direction is keenly desired because large differences of hardness in the steel sheet thickness direction between the surface portion and the central portion significantly deteriorate the punching tool during punching.
To answer these requests, several technologies were studied to improve the workability and homogeneous mechanical properties of high carbon steel sheets.
For example, JP-A-9-157758, (the term “JP-A” referred to herein signifies the “Unexamined Japanese Patent Publication”)), proposed a method for manufacturing high carbon cold-rolled workable steel strip having improved workability by the steps of:                hot-rolling a high carbon steel having a specified chemical composition, followed by descaling therefrom;        annealing the steel in a hydrogen atmosphere (95% or more of hydrogen by volume) while specifying heating rate, soaking temperature (Ac1 transformation point or above), and soaking time depending on the chemical composition;        cooling the annealed steel at cooling rates of 100° C./hr or smaller to prepare a hot-rolled workable steel strip having excellent structural homogeneity and workability (ductility);        cold-rolling the steel strip at rolling reductions from 20 to 90%; and        finish-annealing the steel at temperatures from 600° C. to 720° C. in a nitrogen-atmosphere furnace or the like.        
Furthermore, for example, JP-A-5-9588 proposed a method for manufacturing high carbon cold-rolled steel thin sheet having good workability by the steps of:                rolling a steel at finishing temperatures of (Ac1 transformation point +30° C.) or above to prepare a steel sheet;        cooling the steel sheet to temperatures from 20° C. to 500° C. at cooling rates from 10 to 100° C./s;        holding the steel sheet for 1 to 10 seconds;        reheating the steel sheet to temperatures from 500° C. to (Ac1 transformation point +30° C.), followed by coiling the steel sheet;        soaking the steel sheet, at need, at temperatures from 650° C. to (Ac1 transformation point +30° C.) for 1 hour or more; and        applying a cycle of cold-rolling and annealing at temperatures from 650° C. to (Ac1 transformation point +30° C.) for 1 hour or more, at least once.        
Other than above, as the hot-rolled steel sheets, JP-A-3-174909, for example, proposed a method for manufacturing stably a high carbon hot-rolled steel strip having excellent homogeneous mechanical properties in the longitudinal direction of coil by the steps of:                dividing a hot-run table (or run-out table) into an accelerated cooling zone and an air-cooling zone;        applying accelerated cooling to a finish-rolled steel strip to a specific temperature or below determined by the length of cooling zone, the transfer speed of steel sheet, the chemical composition of the steel, and the like; and then        applying air-cooling to the steel strip.        
The cooling rate in the accelerated cooling zone according to JP-A-3-174909 is about 20 to about 30° C./s suggested by FIG. 3 in the disclosure.
In addition, for example, JP-A-2003-13145 proposed a method for manufacturing high carbon hot-rolled steel sheet having excellent stretch-flanging formability by the steps of:                using a steel containing 0.2 to 0.7% C by mass;        hot-rolling the steel at finishing temperatures of (Ar3 transformation point −20° C.) or above;        cooling the steel sheet at cooling rates of higher than 120° C./s and at cooling-stop temperatures of not higher than 650° C.;        coiling the steel sheet at temperatures of 600° C. or below; and then        annealing the steel sheet at temperatures from 640° C. or larger to Ac1 transformation point or lower.        
Although the object does not agree with that of above examples, JP-A-2003-73742 disclosed a technology for manufacturing high carbon hot-rolled steel sheet which satisfies the above requirements except for selecting the cooling-stop temperature of 620° C. or below. In addition, JP-A-2003-73740 disclosed a technology for manufacturing high carbon cold-rolled steel sheet which satisfies the above requirements except for selecting the cooling-stop temperatures of 620° C. or below and applying the annealing after cold-rolling at rolling reductions of 30% or more.